Ideally, we want the single image estimate of \(\mu _t, \sigma _t\)  to be as close as possible to the true mean and variance of the target distribution. The variance of the above estimators can be reduced by increasing the number of samples. Given that we have only one sample \(\mathrm {x}\)  at hand, we ask the question - is it possible to generate more data points to improve the estimates? While we do not have access to the underlying distribution of the target instances, we can possibly create data points in the vicinity of \(\mathrm {x}\) . Inspired by the recent works in contrastive learning for representation learning [1]} and theoretical justifications of pseudo-labeling [2]}, which suggests that using neighborhood samples via augmentation helps in the respective tasks, we adopt this idea for our task to improve the estimate of target image statistics.
